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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 4, Pages 754–764 (Mi smj2236)  
This article is cited in 1 scientific paper (total in 1 paper)

The functional limit theorem for the canonical $U$-processes defined on dependent trials

I. S. Borisova, V. A. Zhechevb

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (299 kB) Citations (1)
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Abstract: The functional limit theorem is proven for a sequence of normalized $U$-statistics (the socalled $U$-processes) of arbitrary order with canonical (degenerate) kernels defined on samples of $\varphi$-mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.
Keywords: canonical $U$-statistics, invariance principle, stationary sequence of observations, $\varphi$-mixing.
Received: 09.02.2011
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 4, Pages 593–601
DOI: https://doi.org/10.1134/S0037446611040045
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: I. S. Borisov, V. A. Zhechev, “The functional limit theorem for the canonical $U$-processes defined on dependent trials”, Sibirsk. Mat. Zh., 52:4 (2011), 754–764; Siberian Math. J., 52:4 (2011), 593–601
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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